Growth and the diffusion of ideas

Staley, Mark

doi:10.1016/j.jmateco.2011.06.006

Cited by 19 publications

(34 citation statements)

References 36 publications

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“…they presume that individual productivity also fluctuates in the absence of meetings. Similar statements were shown in related works by Alvarez et al, Lucas and Staley in [2,12,18] in the case of Boltzmann type models for knowledge growth. These models are closely related to the BMFG model (5) -they correspond to (2) with a given constant interaction probability α = α 0 .…”

Section: Knowledge Diffusion Leads To Balanced Growthsupporting

confidence: 90%

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Balanced growth path solutions of a Boltzmann mean field game model for knowledge growth

Burger¹,

Lorz²,

Wolfram³

2017

Kinetic &Amp; Related Models

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In this paper we study balanced growth path solutions of a Boltzmann mean field game model proposed by Lucas et al [13] to model knowledge growth in an economy. Agents can either increase their knowledge level by exchanging ideas in learning events or by producing goods with the knowledge they already have. The existence of balanced growth path solutions implies exponential growth of the overall production in time. We proof existence of balanced growth path solutions if the initial distribution of individuals with respect to their knowledge level satisfies a Pareto-tail condition. Furthermore we give first insights into the existence of such solutions if in addition to production and knowledge exchange the knowledge level evolves by geometric Brownian motion. arXiv:1602.01423v2 [math.AP] 30 Mar 2016z 0 α(s)ρ x (y, t) dy with ρ x (z, t ) = δ x . Here S denotes the set of admissible controls given by S = {s : [0, ∞) × [0, T ] → [0, 1]}.

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Section: Knowledge Diffusion Leads To Balanced Growthsupporting

confidence: 90%

“…(32) Equation (32) can be studied in the case of small diffusion, which models innovation by small fluctuations in the individual productivity, see [2,12,18] for more details.…”

Section: Knowledge Diffusion Leads To Balanced Growthmentioning

confidence: 99%

Balanced growth path solutions of a Boltzmann mean field game model for knowledge growth

Burger¹,

Lorz²,

Wolfram³

2017

Kinetic &Amp; Related Models

View full text Add to dashboard Cite

show abstract

“…This growth rate is increasing in the ratio of the location parameter of the initial distribution and the ratio of Note that in the case k 0 =0, it is not possible to have a BGP without having a fat-tailed invariant distribution; otherwise, the economy would eventually run out of ideas. However, even without a fat-tail, as long as there is a growing external or initial source of ideas, or individuals' learning also has a stochastic component, balance growth is attainable (for a recent discussion, see Staley 2011;Luttmer et al 2012;Benhabib et al 2017).…”

Section: Continuous Arrivalsmentioning

confidence: 99%

Note on Idea Diffusion Models with Cohort Structures

Caicedo

2018

Economica

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In this note I propose two alternative frameworks to study idea diffusion models with cohort structures. Both frameworks fix the Lucas (2009) aggregation mistake while keeping the analytical tractability of the model and its insights. The frameworks differ in their assumptions on the meeting process. I study first a continuous arrival process where agents meet at each point in time, and then a more commonly used Poisson process where meeting opportunities arrive stochastically at some given Poisson rate. I generalize the growth formula in Lucas (2009) and show that both models yield the same growth rate on a balanced growth path. Moreover, I show that the continuous arrival process can be viewed as the limit of Poisson processes where the meeting rate increases but the quality of meetings decreases.

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“…The di¤erential equations that govern these examples are degenerate special cases of equations that appear later. Section 3 presents a basic example, inspired by the discussion of scale e¤ects in Staley [2011], of what happens when one combines social learning with individual discovery in a …nite economy. A closely related large economy is introduced in Section 4, following Staley [2011] and Luttmer [2012bLuttmer [ , 2015.…”

Section: Introductionmentioning

confidence: 99%

“…Section 3 presents a basic example, inspired by the discussion of scale e¤ects in Staley [2011], of what happens when one combines social learning with individual discovery in a …nite economy. A closely related large economy is introduced in Section 4, following Staley [2011] and Luttmer [2012bLuttmer [ , 2015. Section 5 considers the basic elements of an economy with entry and exit in which only new entrants can learn from incumbent producers, as in Luttmer [2007].…”

Section: Introductionmentioning

confidence: 99%

Four Models of Knowledge Diffusion and Growth

Luttmer¹

2015

Preprint

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This paper describes how long-run growth emerges in four closely related models that combine individual discovery with some form of social learning. In a large economy, there is a continuum of long-run growth rates and associated stationary distributions when it is possible to learn from individuals in the right tail of the productivity distribution. What happens in the long run depends on initial conditions. Two distinct literatures, one on reaction-diffusion equations, and another on quasi-stationary distributions suggest a unique long-run outcome when the initial productivity distribution has bounded support.

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Growth and the diffusion of ideas

Cited by 19 publications

References 36 publications

Balanced growth path solutions of a Boltzmann mean field game model for knowledge growth

Balanced growth path solutions of a Boltzmann mean field game model for knowledge growth

Note on Idea Diffusion Models with Cohort Structures

Four Models of Knowledge Diffusion and Growth

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